n-way anova produces the same p-value for all groups

I have 6 vectors of values. These are split into groups i and m. There are 3 i groups and 2 m groups, which yields a combination of 6 total groups. Supposedly, my data should indicate that the data I have are grouped better according to 'Hm' vs 'Rm' than 'Li' vs 'Ri' vs 'Hi'. When I run the ANOVA using anovan() I get the same P-value for the i grouping, the m grouping and i*m interaction. When I plot the distributions using a boxplot they are clearly more separable along the m dimension.

All necessary files are attached. I'm using R2021a

I am running:

mdacdlcdp=[cdlcdpLiRm;cdlcdpLiHm;cdlcdpRiRm;cdlcdpRiHm;cdlcdpHiRm;cdlcdpHiHm];
p=anovan(mdacdlcdp,{igroup,mgroup},'model','interaction','varnames',{'i','m'})

But the results shown below are not consistent with my expectations.

  Source               Sum Sq.   d.f.   Mean Sq.     F     Prob>F
-----------------------------------------------------------------
  i                    0.4867     2    0.24335     2.98   0.054 
  m                    1.2762     1    1.27619    15.62   0.054 
  i*m                  0.2255     2    0.11276     1.38   0.054 
  Error                11.7664   144    0.08171                  
  Total                13.7548   149                                                          

[Megumi Fukuda]

I ran these codes with my computer (WIndows, MATLAB 2021a)

load('anovadata.mat')
load('igroup.mat')
load('mgroup.mat')
mdacdlcdp=[cdlcdpLiRm;cdlcdpLiHm;cdlcdpRiRm;cdlcdpRiHm;cdlcdpHiRm;cdlcdpHiHm];
p=anovan(mdacdlcdp,{igroup,mgroup},'model','interaction','varnames',{'i','m'})

and got these results. Could you confirm you run your code correctly?

  Source   Sum Sq.   d.f.   Mean Sq.     F     Prob>F
-----------------------------------------------------
  i         0.4867     2    0.24335     2.98   0.054 
  m         1.2762     1    1.27619    15.62   0.0001
  i*m       0.2255     2    0.11276     1.38   0.2549
  Error    11.7664   144    0.08171                  
  Total    13.7548   149                             

[AbioEngineer]

Thank you for your reply. I ran the exact same code as you, copied and pasted from your response, but got the same results as before. Is there a low level problem with my computer? I also have 2020b installed, but it gives me the same results as 2021a. I have rebooted my PC too, but no luck.

Answer 1

[AbioEngineer]

One of the toolboxes I permanently added to my startup path was causing the problem. I muted all the starup addpaths and it worked like normal. Sorry for all the fuss

[Varun Wadia]

Hi! I'm having the same issue do you know which toolbox it was? Thank you!